tains 180 degrees. Thus, AC is a quadrant, and ACB is a semi-circumference. 30. If one straight line meets another, what is the sum of the two angles equal to? If a straight line EB meets another straight line AC, the sum of the angles ABE and EBC, will be equal to two right angles, since these two E A angles are measured by half the circumference. 31. If there be several angles, what will their sum be equal to? If there be several angles CBF, FBE, EBD, DBA, formed on the same side of a line, their sum, for a like reason, will be equal to two right angles. F E B 32. What is the sum of all the angles formed about a point equal to? The sum of all the angles ACB, BCD, DCA, which can be formed about any point as C, is equal to four right angles, or 360 degrees, since they are measured by the entire circumference. SECTION II. OF PLANE FIGURES. 1. What is a plane figure? A plane figure is a portion of a plane, terminated on all sides by lines, either straight or curved. 2. When the bounding lines are straight, what is it called? If the bounding lines are straight, the space they enclose is called a rectilineal figure, or polygon. 3. What are the lines themselves called? The lines themselves, taken together, are called the perimeter of the polygon. Hence, the perimeter of a polygon is the sum of all its sides. 4. Name the different kinds of polygons. A polygon of three sides, is called a triangle. A polygon of four sides, is called a quadrilateral. A polygon of five sides, is called a pentagon. A polygon of six sides, is called a 'hexagon. A polygon of seven sides, is called a heptagon. 5. What is the perimeter of a polygon? The perimeter of a polygon is the sum of all its sides. 6. What is the least number of straight lines which can enclose a space? Three straight lines, are the smallest number which can enclose a space. 7. Name the several kinds of triangles. First.-An equilateral triangle, which has its three sides all equal. Second. An isosceles triangle, which has two of its sides equal. Third. A scalene triangle, which has its three sides all unequal. Fourth. A right-angled triangle, which has one right angle. In the right-angled triangle BAC, the side BC opposite the right angle, is called the hypothenuse. B 8. What is the base of a triangle?—what its altitude? The base of a triangle is the side on which it stands. Thus, BA is the base of the right-angled triangle BAC. The line drawn from the opposite angle perpendicular to the base, is called the altitude. Thus, AC is the altitude. 9. Name the different kinds of quadrilaterals. First. The square, which has all its sides equal, and all its angles right angles. Second. The rectangle, which has its angles right angles, and its opposite sides equal and parallel. Third. The parallelogram, which has its opposite sides equal and parallel, but its angles not right angles. Fourth. The rhombus, which has all its sides equal, and the opposite sides parallel, without having its angles right angles. Fifth. The trapezoid, which has only two of its sides parallel. 10. What is the base of a figure? What its altitude? The base of a figure is the side on which it stands, and the altitude is a line drawn from the top, perpendicular to the base. 11. What is a diagonal? A diagonal, is a line joining the vertices of two angles not adjacent. Thus, AB is a diagonal. 12. What is the square described on the hypothenuse of a right-angled triangle equal to? In every right-angled triangle, the square described on the hypothenuse, is equal to the sum of the squares described on the other two sides. Thus, if ABC be a rightangled triangle, right-angled at C, then will the square D, described on AB, be equal to the sum of the squares E and F, described on the sides CB and AC. This is called the carpenter's theorem. B D By counting the small squares in the large square D, you will find their number equal to that contained in the small squares F and E. |
